Rocket Staging (propulsion/rocket/rocket-staging)
Use when the task is multi-stage rocket staging: per-stage ideal
delta-v, stage mass ratio and payload fraction allocation, structural
index, and stage optimization for a target total delta-v.
Domain quick reference
- Per-stage ideal delta-v from the rocket equation:
delta-v = g0 * Isp * ln(m0 / mf), with g0 = 9.80665 m/s^2.
- Worked: Isp = 300 s and m0 / mf = 2 give
delta-v = 9.80665 * 300 * ln(2) = 2039.24 m/s.
- Stage mass ratio from a delta-v requirement:
m0 / mf = exp(delta-v / (g0 * Isp)). Worked: 2040 m/s at Isp = 300 s
gives m0 / mf = 2.00.
- Structural index eps = m_struct / (m_struct + m_prop). Worked:
10000 kg structure and 90000 kg propellant give eps = 0.1.
- Payload fraction lam = m_payload / m0. Worked: 5000 kg payload on a
100000 kg stage gives lam = 0.05.
- Stage mass ratio from the allocation indices:
m0 / mf = 1 / (lam + eps * (1 - lam)). Worked: eps = 0.1 and lam =
0.05 give m0 / mf = 6.8966 and delta-v = 5681.06 m/s at Isp = 300 s.
- Equal-stage optimum split for a target total delta-v:
r* = exp(dv_total / (n * g0 * Isp)); every stage takes the same ratio
and the total payload fraction is lam^n with
lam = (1 / r* - eps) / (1 - eps). Worked: 9000 m/s, 2 stages, Isp =
300 s, eps = 0.1 give r* = 4.6162 and lam_total = 0.01679.
- Minimum stage count for a payload target: 9000 m/s at Isp = 300 s
and eps = 0.1 needs 3 stages for lam_total >= 0.02 (3 stages give
0.0243). The achievable payload fraction is bounded by
exp(-dv_total / (g0 * Isp * (1 - eps))) = 0.0334 as the stage count
grows, so a 0.05 target is infeasible.
Workflow
- Collect the target total delta-v, the per-stage specific impulse,
the structural indices, and the payload mass.
- Compute each stage delta-v with stage_delta_v, or convert a stage
delta-v requirement to a stage mass ratio with mass_ratio_from_delta_v.
- Allocate the payload fraction and the structural index with
payload_fraction and structural_index; combine them with
mass_ratio_from_indices.
- Check the per-stage delta-v implied by the allocation with
stage_delta_v_from_indices.
- Optimize the split of identical stages with
optimal_equal_stage_split.
- Find the minimum stage count for the payload target with
stage_count_for_delta_v; sum per-stage delta-v with
total_staged_delta_v.
Pitfalls
- Confusing the structural index eps (inert fraction of the dry stage)
with the payload fraction lam (payload over initial stage mass).
- Using the full-vehicle mass ratio in every stage: each stage burns
with only the stages above it as payload, so each stage has its own
mass ratio.
- Forgetting that stage payload fractions multiply, not add: the total
payload fraction is lam^n, which is why 2 stages with lam = 0.13 give
only 1.68% total payload.
- Treating the single-stage rocket equation as the staging answer:
staging exists precisely because one stage cannot carry both the
propellant and the structure for a large delta-v.
- Assuming more stages are always better: the payload fraction
saturates at exp(-dv_total / (g0 * Isp * (1 - eps))), and each extra
stage adds separation mass and failure modes.
- Confusing this leaf with rocket-sizing (which sizes the propellant
mass and sums stage delta-v), with nozzle-design (which sizes the
nozzle area ratio and exit Mach), or with propellant-selection
(which trades propellant families and density impulse).
- Using inconsistent units: Isp in seconds, masses in kg, delta-v in
m/s, with g0 = 9.80665 m/s^2.
Behavior contract (gate 3)
The staging logic is exercised by the gate 3 contract test:
scripts/test_rocket_staging.py against scripts/rocket_staging_logic.py
(stdlib unittest, offline). Run:
python3 skills/propulsion/rocket/rocket-staging/scripts/test_rocket_staging.py
Compliance
- Standards referenced, not reproduced: ECSS space-systems standards
frame the launch-vehicle engineering context (free ESA download,
ecss.nl/standards); the rocket equation and the staging optimum are
common propulsion methodology, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.
1---2name: rocket-staging3description: Use when you must analyze multi-stage rocket staging for a launch vehicle: compute the ideal delta-v per stage from the rocket equation, allocate the stage mass ratios and the payload fraction across the stages, derive the structural index from the inert and the propellant masses, and optimize the stage count for a target total delta-v. Produces the per-stage delta-v, the stage mass ratio, the stage payload fraction, the structural index, the optimal stage split, and the minimum stage count, in SI units. Applies the equal-stage optimum split for identical stages. Trigger: rocket staging, stage mass ratio, payload fraction, structural index, stage count, delta-v.4license: Apache-2.05---67# Rocket Staging (propulsion/rocket/rocket-staging)89Use when the task is multi-stage rocket staging: per-stage ideal10delta-v, stage mass ratio and payload fraction allocation, structural11index, and stage optimization for a target total delta-v.1213## Domain quick reference1415- Per-stage ideal delta-v from the rocket equation:16 delta-v = g0 * Isp * ln(m0 / mf), with g0 = 9.80665 m/s^2.17- Worked: Isp = 300 s and m0 / mf = 2 give18 delta-v = 9.80665 * 300 * ln(2) = 2039.24 m/s.19- Stage mass ratio from a delta-v requirement:20 m0 / mf = exp(delta-v / (g0 * Isp)). Worked: 2040 m/s at Isp = 300 s21 gives m0 / mf = 2.00.22- Structural index eps = m_struct / (m_struct + m_prop). Worked:23 10000 kg structure and 90000 kg propellant give eps = 0.1.24- Payload fraction lam = m_payload / m0. Worked: 5000 kg payload on a25 100000 kg stage gives lam = 0.05.26- Stage mass ratio from the allocation indices:27 m0 / mf = 1 / (lam + eps * (1 - lam)). Worked: eps = 0.1 and lam =28 0.05 give m0 / mf = 6.8966 and delta-v = 5681.06 m/s at Isp = 300 s.29- Equal-stage optimum split for a target total delta-v:30 r* = exp(dv_total / (n * g0 * Isp)); every stage takes the same ratio31 and the total payload fraction is lam^n with32 lam = (1 / r* - eps) / (1 - eps). Worked: 9000 m/s, 2 stages, Isp =33 300 s, eps = 0.1 give r* = 4.6162 and lam_total = 0.01679.34- Minimum stage count for a payload target: 9000 m/s at Isp = 300 s35 and eps = 0.1 needs 3 stages for lam_total >= 0.02 (3 stages give36 0.0243). The achievable payload fraction is bounded by37 exp(-dv_total / (g0 * Isp * (1 - eps))) = 0.0334 as the stage count38 grows, so a 0.05 target is infeasible.3940## Workflow41421. Collect the target total delta-v, the per-stage specific impulse,43 the structural indices, and the payload mass.442. Compute each stage delta-v with stage_delta_v, or convert a stage45 delta-v requirement to a stage mass ratio with mass_ratio_from_delta_v.463. Allocate the payload fraction and the structural index with47 payload_fraction and structural_index; combine them with48 mass_ratio_from_indices.494. Check the per-stage delta-v implied by the allocation with50 stage_delta_v_from_indices.515. Optimize the split of identical stages with52 optimal_equal_stage_split.536. Find the minimum stage count for the payload target with54 stage_count_for_delta_v; sum per-stage delta-v with55 total_staged_delta_v.5657## Pitfalls5859- Confusing the structural index eps (inert fraction of the dry stage)60 with the payload fraction lam (payload over initial stage mass).61- Using the full-vehicle mass ratio in every stage: each stage burns62 with only the stages above it as payload, so each stage has its own63 mass ratio.64- Forgetting that stage payload fractions multiply, not add: the total65 payload fraction is lam^n, which is why 2 stages with lam = 0.13 give66 only 1.68% total payload.67- Treating the single-stage rocket equation as the staging answer:68 staging exists precisely because one stage cannot carry both the69 propellant and the structure for a large delta-v.70- Assuming more stages are always better: the payload fraction71 saturates at exp(-dv_total / (g0 * Isp * (1 - eps))), and each extra72 stage adds separation mass and failure modes.73- Confusing this leaf with rocket-sizing (which sizes the propellant74 mass and sums stage delta-v), with nozzle-design (which sizes the75 nozzle area ratio and exit Mach), or with propellant-selection76 (which trades propellant families and density impulse).77- Using inconsistent units: Isp in seconds, masses in kg, delta-v in78 m/s, with g0 = 9.80665 m/s^2.7980## Behavior contract (gate 3)8182The staging logic is exercised by the gate 3 contract test:83scripts/test_rocket_staging.py against scripts/rocket_staging_logic.py84(stdlib unittest, offline). Run:85python3 skills/propulsion/rocket/rocket-staging/scripts/test_rocket_staging.py8687## Compliance8889- Standards referenced, not reproduced: ECSS space-systems standards90 frame the launch-vehicle engineering context (free ESA download,91 ecss.nl/standards); the rocket equation and the staging optimum are92 common propulsion methodology, summary-only per standards-map.yaml.93- compliance: STANDARDS-REF, gated: false.
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